Function Name: f5

************************** Initial Input Values: ********************************
x_0= -2.000000e+000, x_1=2.000000e+000, f(x_0)= -1.000000e+000, f(x_1)= -1.000000e+000 
*********************************************************************************

n= 0 a= -2.000000e+000, f(a)= -1.000000e+000 
n= 1 a= 2.000000e+000, f(a)= -1.000000e+000 

*** ERROR ocurred: Division by Zero - Function values of
*** both points were the same. 
True answer could not be obtained. No values were assigned
to the return constructs.
??? One or more output arguments not assigned during call to 'secant'.

Error in ==> D:\MATLAB6p5\work\run_me5.m
On line 25  ==> [r,sequence_x,sequence_fx]=secant('f5',x_0,x_1,n_max,secant_tolerance);

>>

************************** Initial Input Values: ********************************
x_0= -1.700000e+000, x_1=-2.000000e+000, f(x_0)= -8.183306e-001, f(x_1)= -1.000000e+000 
*********************************************************************************

n= 0 a= -1.700000e+000, f(a)= -8.183306e-001 
n= 1 a= -2.000000e+000, f(a)= -1.000000e+000 
n= 2, a= -3.486486e-001, f(a)= -5.631617e-001 
n= 3, a= 2.633805e+000, f(a)= -2.423572e+000 
n= 4, a= -1.251462e+000, f(a)= -6.725997e-001 
n= 5, a= 4.297181e+000, f(a)= 5.282194e-001 
n= 6, a= 2.048638e+000, f(a)= -1.040998e+000 
n= 7, a= 3.540292e+000, f(a)= 1.414961e+000 
n= 8, a= 4.748049e+000, f(a)= 3.691680e-001 
n= 9, a= 5.794541e+000, f(a)= 2.034447e-001 
n= 10, a= 7.079232e+000, f(a)= 1.216086e-001 
n= 11, a= 8.988285e+000, f(a)= 6.964830e-002 
n= 12, a= 1.154721e+001, f(a)= 4.021297e-002 
n= 13, a= 1.504307e+001, f(a)= 2.301031e-002 
n= 14, a= 1.971914e+001, f(a)= 1.316328e-002 
n= 15, a= 2.597001e+001, f(a)= 7.513812e-003 
n= 16, a= 3.428368e+001, f(a)= 4.286803e-003 
n= 17, a= 4.532767e+001, f(a)= 2.444274e-003 
n= 18, a= 5.997848e+001, f(a)= 1.393372e-003 
n= 19, a= 7.940372e+001, f(a)= 7.941612e-004 
n= 20, a= 1.051489e+002, f(a)= 4.525998e-004 
n= 21, a= 1.392636e+002, f(a)= 2.579269e-004 
n= 22, a= 1.844629e+002, f(a)= 1.469829e-004 
n= 23, a= 2.443448e+002, f(a)= 8.375860e-005 
n= 24, a= 3.236754e+002, f(a)= 4.772963e-005 
n= 25, a= 4.287691e+002, f(a)= 2.719846e-005 
n= 26, a= 5.679910e+002, f(a)= 1.549884e-005 
n= 27, a= 7.524225e+002, f(a)= 8.831885e-006 
n= 28, a= 9.967435e+002, f(a)= 5.032770e-006 
n= 29, a= 1.320401e+003, f(a)= 2.867878e-006 
n= 30, a= 1.749157e+003, f(a)= 1.634233e-006 
n= 31, a= 2.317137e+003, f(a)= 9.312520e-007 
n= 32, a= 3.069552e+003, f(a)= 5.306650e-007 
n= 33, a= 4.066290e+003, f(a)= 3.023943e-007 
n= 34, a= 5.386686e+003, f(a)= 1.723165e-007 
n= 35, a= 7.135839e+003, f(a)= 9.819287e-008 
n= 36, a= 9.452974e+003, f(a)= 5.595425e-008 
n= 37, a= 1.252252e+004, f(a)= 3.188499e-008 
n= 38, a= 1.658881e+004, f(a)= 1.816935e-008 
n= 39, a= 2.197550e+004, f(a)= 1.035363e-008 
n= 40, a= 2.911134e+004, f(a)= 5.899915e-009 
n= 41, a= 3.856431e+004, f(a)= 3.362009e-009 
n= 42, a= 5.108683e+004, f(a)= 1.915808e-009 
n= 43, a= 6.767565e+004, f(a)= 1.091705e-009 
n= 44, a= 8.965114e+004, f(a)= 6.220973e-010 
n= 45, a= 1.187625e+005, f(a)= 3.544961e-010 
n= 46, a= 1.573268e+005, f(a)= 2.020062e-010 
n= 47, a= 2.084136e+005, f(a)= 1.151113e-010 
n= 48, a= 2.760893e+005, f(a)= 6.559503e-011 
n= 49, a= 3.657404e+005, f(a)= 3.737869e-011 
n= 50, a= 4.845029e+005, f(a)= 2.129988e-011 
n= 51, a= 6.418297e+005, f(a)= 1.213753e-011 
n= 52, a= 8.502433e+005, f(a)= 6.916455e-012 
n= 53, a= 1.126333e+006, f(a)= 3.941275e-012 
n= 54, a= 1.492073e+006, f(a)= 2.245897e-012 
n= 55, a= 1.976576e+006, f(a)= 1.279803e-012 
n= 56, a= 2.618406e+006, f(a)= 7.292831e-013 
n= 57, a= 3.468649e+006, f(a)= 4.155749e-013 
n= 58, a= 4.594981e+006, f(a)= 2.368113e-013 
n= 59, a= 6.087054e+006, f(a)= 1.349446e-013 
n= 60, a= 8.063630e+006, f(a)= 7.689689e-014 
n= 61, a= 1.068204e+007, f(a)= 4.381895e-014 
n= 62, a= 1.415068e+007, f(a)= 2.496980e-014 
n= 63, a= 1.874567e+007, f(a)= 1.422880e-014 
n= 64, a= 2.483272e+007, f(a)= 8.108143e-015 
n= 65, a= 3.289635e+007, f(a)= 4.620347e-015 
n= 66, a= 4.357839e+007, f(a)= 2.632860e-015 
n= 67, a= 5.772907e+007, f(a)= 1.500309e-015 
n= 68, a= 7.647474e+007, f(a)= 8.549368e-016 
n= 69, a= 1.013075e+008, f(a)= 4.871774e-016 
n= 70, a= 1.342038e+008, f(a)= 2.776133e-016 
n= 71, a= 1.777822e+008, f(a)= 1.581953e-016 
n= 72, a= 2.355113e+008, f(a)= 9.014603e-017 
n= 73, a= 3.119860e+008, f(a)= 5.136884e-017 
n= 74, a= 4.132935e+008, f(a)= 2.927204e-017 
n= 75, a= 5.474973e+008, f(a)= 1.668039e-017 
n= 76, a= 7.252795e+008, f(a)= 9.505156e-018 
n= 77, a= 9.607907e+008, f(a)= 5.416421e-018 
n= 78, a= 1.272777e+009, f(a)= 3.086495e-018 
n= 79, a= 1.686070e+009, f(a)= 1.758809e-018 
n= 80, a= 2.233567e+009, f(a)= 1.002240e-018 
n= 81, a= 2.958847e+009, f(a)= 5.711169e-019 
n= 82, a= 3.919638e+009, f(a)= 3.254454e-019 
n= 83, a= 5.192414e+009, f(a)= 1.854519e-019 
n= 84, a= 6.878485e+009, f(a)= 1.056780e-019 
n= 85, a= 9.112052e+009, f(a)= 6.021956e-020 
n= 86, a= 1.207090e+010, f(a)= 3.431553e-020 
n= 87, a= 1.599054e+010, f(a)= 1.955437e-020 
n= 88, a= 2.118295e+010, f(a)= 1.114287e-020 
n= 89, a= 2.806144e+010, f(a)= 6.349656e-021 
n= 90, a= 3.717349e+010, f(a)= 3.618290e-021 
n= 91, a= 4.924439e+010, f(a)= 2.061847e-021 
n= 92, a= 6.523492e+010, f(a)= 1.174924e-021 
n= 93, a= 8.641788e+010, f(a)= 6.695189e-022 
n= 94, a= 1.144793e+011, f(a)= 3.815188e-022 
n= 95, a= 1.516528e+011, f(a)= 2.174048e-022 
n= 96, a= 2.008972e+011, f(a)= 1.238860e-022 
n= 97, a= 2.661321e+011, f(a)= 7.059524e-023 
n= 98, a= 3.525500e+011, f(a)= 4.022801e-023 
n= 99, a= 4.670293e+011, f(a)= 2.292354e-023 

From the produced graph it can be seen that the slope gets very steep after the 4th iteration, which make the result to converge very fast. 

Therefore, the shown convergence is superlinear.

Files used:      f4_1.m        run_me4_1_2.m

Based on the same assertions, the received convergence is also superlinear.